3.1 Acquired spectra
We first compare the different spectra, acquired from a single molecule in both filter configurations. When a single molecule was identified in the confocal microscope, the spectrometer was introduced and a spectrum was acquired. Figure 2(a) shows the single molecule spectra in both filter configurations. The filtering with the atomic vapor shows the entire spectrum of the single molecule as it would be excited with a more blue wavelength. On first sight, this violates energy conservation, but most likely the more blue components are introduced by anti-Stokes processes. On the other hand, we find the spectrum acquired with the commercial 593 nm long-pass filter to be cutoff until 600 nm. Furthermore, compared to the spectrum provided by the dye producer, we find the single molecule fluorescence to be spectral shifted to the blue by about 5 nm. This is not untypical for organic dyes that their fluorescent properties critically depend on their chemical environment [34, 35].
Assuming the quantum efficiency of the single photon detector is a fixed value in the range of 570-700 nm, we can directly compare the integral contribution of the dye spectra as proportional to the detected signal on the photo detector. The result is a 15.5% higher signal with atomic filtering than with a commercial long-pass filter.
Unfortunately, although the sodium vapor filter increases the overall signal from the molecule studied, it also introduced a higher laser background. In particular we find around 20 times increased laser background even though the optical rejection is calculated to be much higher than with the commercial filter. There are two explanations for this finding: (a) the filter does not have such a high rejection due to non-linearities or saturation effects in the vapor. Or, (b), the atomic filter or some components of our setup (e.g.: laser, optical fiber, sample) spectral shifts the scattered light far enough away from the laser wavelength that it cannot be blocked. To investigate this problem, we performed simple measurements of the atomic filter with laser light via bypassing the microscope with a mirror. This resulted in a measured optical rejection of more than 6 orders of magnitude. It was necessary to perform the measurements above the saturation intensity (9.4 mW/cm2) to determine the optical rejection of the filter due to the weak signal. Generally, a weak laser background contribution is not relevant for the acquisition of single molecule signals, since this simply adds a constant background, as long as laser power fluctuations are not too large. Following this assumption the background can be simply subtracted.
3.2 Data analysis
In the following paragraph we introduce the protocol for data analysis. For both, the confocal and the wide-field imaging, data processing was performed as follows: Since the main goal was to compare the two filter configurations, an image was acquired with each filter at the exact same settings (excitation intensity, acquisition time, etc.). Both images were acquired with minimal time delay and usually an acquisition sequence alternating several times between the commercial filter and the atomic filter was used. To avoid additional systematic errors, for example by photobleaching or mechanical drift out of the objective plane, also the filter which was used first had been alternated from sequence to sequence. Then we compared within a sequence the directly following images. The two corresponding images were processed by an automated peak-find routine to identify the molecules. Then molecule pairs were identified by direct correlation of all emitter positions in a corresponding set of images (with the commercial and the atomic filter). The algorithm checks for the nearest neighbor in both images and saves the result with a unique pair ID. Several emitters too close to each other in one image (±3 pixel) were not considered for further evaluations. In addition, all results (emitter pair correlations) had to be checked and confirmed manually. Each identified emitter, which belongs to a former defined pair, was then fitted by using the least-square method to a 2D-Gaussian (symmetric in x and y). The extracted fit parameters are used for further analysis. Note, that we only consider the changes we find for the directly correlated pairs. Since the molecules tend to bleach and blink at ambient conditions, this required a statistical analysis. To determine if molecules are brighter or dimmer after change the filter, we define the quantity relative enhancement ΔI as shown in equation (1):
$$ \Delta I = \frac{ I_{\mathrm{vapor}}-I_{\mathrm{comm}}}{1/2 \cdot (I_{\mathrm{vapor}}+I_{\mathrm{comm}})} . $$
(1)
In case of the confocal configuration \(I_{\mathrm{vapor}}\) and \(I_{\mathrm{comm}}\) are the maximum of the fitted 2D-Gaussian for the vapor cell and the commercial filter, respectively. In case of the wide-field configuration \(I_{\mathrm{vapor}}\) and \(I_{\mathrm{comm}}\) are the integrals of the fitted 2D-Gaussian. This is attributed to the information content of the images: In the confocal case one obtains the integrated signal from the maximum of the emitter position; whereas in the case of the wide-field one acquires a photon distribution which obeys the point spread function of the system. Subsequently, an integration of the signal is required before the total photon flux is accessible.
To estimate the background and its fluctuation, all images were analyzed in an area where no molecules were present. Due to the fact that we can analyze many more molecules than images, the statistical fluctuation is higher. With this data, a histogram of signal to background (SBR) and signal to noise (SNR) ratios can be determined. Any fluctuation in the molecules emission rate was not accounted for. Assuming a non-fluctuating background contribution, this can be simply subtracted from the original data. The analysis presented below is always a statistical comparison between both filter configurations and many co-localized single molecules.
3.3 Confocal imaging
Now we turn to the confocal configuration of the microscope. Initially, the experimental configuration was set up differently than shown in Figure 1(b): The filters were placed between the microscope and the pinhole. However, severe power fluctuations were found in the single molecule signals acquired with the atomic filter on the order of one magnitude. Due to hot air convection surrounding the vapor cell, the collimated beam wanders on the pinhole. Therefore, the confocal configuration was changed and the atomic filter was placed between the pinhole and the single photon detector. This configuration is also described in [26]. To estimate the fluctuation of the wandering beam on the detector, we placed a camera at the location of the avalanche photo diode and monitor the fluorescence of a dense labeled DNA droplet. At high speed (10 ms), a 71 μm spot size (\(1/\mathrm{e}^{2}\)) is observed, which is the same as if no thermal fluctuations are present. With an integration over 60 s, a spot size of 82 μm is observed. The used avalanche photo diode has an active detector size of around 170 μm, so the configuration of the vapor cell behind the pinhole does not alter the performance of our setup. We experience no reduction in the spatial resolution compared to the commercial filter. For the vapor cell we find the point spread function of individual emitters to have an average full width half maximum (FWHM) of 291 nm compared to 294 nm with the commercial filter. For comparison the Airy disk should have a radius of around 277 nm for the given experimental parameters.
A raw confocal image of the single molecule sample in both filter configurations is shown in Figure 3(a) and (b). Single step blinking of a molecule is observed in the commercial filter configuration (\(x,y=4\), 8.5 μm). Visually, both images are comparable, but a higher background contribution around 15 kcps is observed in atomic filtering vs. very stable 2 kcps with the commercial filter. This leads to a relative increase of the background by a factor of 7.5 with the atomic filter. Subsequently, we also estimate the signal to noise ratio to be an order of magnitude larger with the commercial filter (SNR = 800!). This is different than in the experiments under cryogenic conditions [29]. The increase in excitation power at ambient conditions (μW instead of nW at cryogenic conditions) seem to have an influence on the signal to noise ratio. This could be a hint, that saturation effects in the vapor increases the background.
The line cuts in Figure 3(c) illustrate the background level. The image background acquired with atomic filtering is higher by a factor of 7-8 based on a laser-power of 1 μW into the microscope. This is fully consistent with the measurements of the optical density: The commercial filter shows an optical density of about seven, whereas the atomic vapor cell was determined to show six orders of magnitude optical suppression.
In an statistical analysis of 963 molecules, when each molecule is compared in both filter configurations, we observe an enhancement in the overall detected counts per emitter of 15.4% (calculated by using equation (1)). Figure 5(a) shows a histogram for all recorded molecule pairs. The statistical error defined as \(\sigma/ \sqrt{N}\) is 1.5%. The atomic filter therefore increases the number of collected photons, but the background suppression is one order of magnitude smaller for the vapor cell to the commercial filter.
3.4 Wide-field imaging
In the wide-field experiment no pinhole is introduced. Therefore, clipping of a wandering beam is not critical. Instead, convection of hot air originating from the vapor cell leads to a shifted or blurred image. In fact, the image is found slightly blurred. The average FWHM of the fluorescence molecules for the atomic cell is 427 nm and for the commercial filter 365 nm. Following the Rayleigh criteria this would clearly result in a reduction of the resolution for the atomic vapor cell compared to the confocal configuration. For localization spectroscopic methods [5, 6] also the number of detected photons directly influences the localization precision: For the used filters one would find a reduction of 10% compared to 17% when only considering the Rayleigh criteria. Of course, this implies that one can treat the wandering of the beam on the CCD chip as a stochastic distribution within the measurement time.
The images looks as in previous case comparable between the two filter configurations (Figure 4(a) and (b)). The background contribution in the atomic filter case is increased, but not as significant as in the confocal configuration. In an analysis of all acquired images, the mean background contribution is increased by 30% from 70 to 100 cps. This increase is also visible in the line-cut shown in Figure 4(c).
For the detection efficiency calculated by integrating over the emitters point spread function, an enhancement of 18.7% with a standard deviation of \(\sigma=28.4\)% is observed. Taking 2,337 measured molecules into account, this leads to a statistical uncertainty of 0.6%. The noise level of the commercial filter and sodium filter is determined to be 30 vs. 40 photons per seconds, based on a laser excitation of 50 μW into the microscope. The increased noise of the atomic filter tends to lower the SNR. However, the higher signal not only compensates this drawback, but gives an increase in the SNR. We find an SNR of 60 for atomic filtering vs. 31 with the commercial filter. The intrinsic noise level of the camera is at least one order of magnitude less and does not play a role here. In summary, we achieve an increased signal, as well as an increased signal to noise ratio for the atomic filter vs. the commercial filter in the wide-field imaging configuration.
3.5 Overall enhancement
Figure 5 shows a histogram of the determined integrated count rates for the commercial and the atomic filtering schemes. Molecules tend to blink and bleach and it is possible that a molecule was fully bright in one image and much dimmer in the next image, acquired with the other filter. The higher fluctuation on the camera (wandering image) leads to an increased spread of the resulting count rate. Therefore, a much wider distribution than in the confocal case is observed. Another important factor is the signal to noise ratio (SNR) in the analyzed image. When e.g. the background noise in the image is higher, the resulting fit outcome for a single molecule shows higher fluctuations. Thereby, Figure 5 does not only represent the overall enhancement of the signal, but also represents the SNR.
In summary, the confocal images show a lower SNR and SBR for an atomic vapor cell filter compared to a commercial filter. But the lateral spread of the molecules does not change and we find an enhancement in the total number detected photons of 15.4 ± 1.5%.
The wide-field images show a comparable SBR for both filters. For wide-field applications the vapor-cell filter exhibits a better detection efficiency than the commercial filter by 18.7 ± 0.6% for the total detected signal and a factor two increased SNR.
In both configurations, atomic filtering results in an enhancement of the number of detectable photons on the order of 15%. This is fully consistent with the single molecule spectra as shown in Figure 2(a), which also indicate an overall enhancement of approximately 15%.